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A constructive converse Lyapunov theorem on exponential stability
1.  Department of Theoretical Physics, GerhardMercatorUniversity, Duisburg, D47057, Germany 
[1] 
Michael Schönlein. Asymptotic stability and smooth Lyapunov functions for a class of abstract dynamical systems. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 40534069. doi: 10.3934/dcds.2017172 
[2] 
Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of firstorder ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 281298. doi: 10.3934/dcdsb.2014.19.281 
[3] 
Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete & Continuous Dynamical Systems  B, 2015, 20 (8) : 23332360. doi: 10.3934/dcdsb.2015.20.2333 
[4] 
Luis Barreira, Claudia Valls. Stability of nonautonomous equations and Lyapunov functions. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 26312650. doi: 10.3934/dcds.2013.33.2631 
[5] 
Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sumofsquares programming. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 939956. doi: 10.3934/dcdsb.2018049 
[6] 
Volodymyr Pichkur. On practical stability of differential inclusions using Lyapunov functions. Discrete & Continuous Dynamical Systems  B, 2017, 22 (5) : 19771986. doi: 10.3934/dcdsb.2017116 
[7] 
Huijuan Li, Robert Baier, Lars Grüne, Sigurdur F. Hafstein, Fabian R. Wirth. Computation of local ISS Lyapunov functions with low gains via linear programming. Discrete & Continuous Dynamical Systems  B, 2015, 20 (8) : 24772495. doi: 10.3934/dcdsb.2015.20.2477 
[8] 
Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete & Continuous Dynamical Systems  B, 2012, 17 (1) : 3356. doi: 10.3934/dcdsb.2012.17.33 
[9] 
Janusz Mierczyński, Sylvia Novo, Rafael Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure & Applied Analysis, 2020, 19 (4) : 22352255. doi: 10.3934/cpaa.2020098 
[10] 
Jean Mawhin, James R. Ward Jr. Guidinglike functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 3954. doi: 10.3934/dcds.2002.8.39 
[11] 
Fuke Wu, George Yin, Le Yi Wang. Razumikhintype theorems on moment exponential stability of functional differential equations involving twotimescale Markovian switching. Mathematical Control & Related Fields, 2015, 5 (3) : 697719. doi: 10.3934/mcrf.2015.5.697 
[12] 
Tomasz Kapela, Piotr Zgliczyński. A Lohnertype algorithm for control systems and ordinary differential inclusions. Discrete & Continuous Dynamical Systems  B, 2009, 11 (2) : 365385. doi: 10.3934/dcdsb.2009.11.365 
[13] 
Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discretetime dynamical systems. Discrete & Continuous Dynamical Systems  B, 2021, 26 (1) : 299336. doi: 10.3934/dcdsb.2020331 
[14] 
Stefano Maset. Conditioning and relative error propagation in linear autonomous ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 28792909. doi: 10.3934/dcdsb.2018165 
[15] 
Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control & Related Fields, 2018, 8 (3&4) : 809828. doi: 10.3934/mcrf.2018036 
[16] 
Doan Thai Son. On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31133126. doi: 10.3934/dcdsb.2017166 
[17] 
Frédéric Mazenc, Christophe Prieur. Strict Lyapunov functions for semilinear parabolic partial differential equations. Mathematical Control & Related Fields, 2011, 1 (2) : 231250. doi: 10.3934/mcrf.2011.1.231 
[18] 
Kazuyuki Yagasaki. Optimal control of the SIR epidemic model based on dynamical systems theory. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021144 
[19] 
Giovanni Russo, Fabian Wirth. Matrix measures, stability and contraction theory for dynamical systems on time scales. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021188 
[20] 
Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linearquadratic optimal control problem with secondorder linear ordinary differential equation of state variable. Numerical Algebra, Control & Optimization, 2021, 11 (4) : 495512. doi: 10.3934/naco.2020040 
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